181

The study of the punching cards mechanism with SolidWorks

Motion

Dorian Nedelcu, Gilbert-Rainer Gillich, Istvan Biro, Zoltan-Iosif

Korka, Attila Gerocs

The objective of the paper is to calculate the velocities and

accelerations for some points of the punching cards mechanism and to

compare the results calculated through grapho-analytical method with

the SolidWorks Motion results.

Keywords: Mechanism, punching cards, SolidWorks Motion

1. Introduction

A punched card is a simple piece of paper stock which was widely used in the

last century in computers or machines organized as semiautomatic data processing

systems [1], [2]. They contain digital information represented by the presence or

absence of holes in predefined positions.

The punching cards mechanism transforms the circular movement of the

leading element OA into a translation of the driven element point M. The kinematic

parameters of the mechanism are the linear velocities and accelerations.

The aim of the present paper was to assess the grapho-analytical method and

the facilities of the Motion module from SolidWord (SW) software for the

kinematic calculus of the main points of a punching card mechanism.

2. The geometry and main parameters of the punching cards mechanism

The geometry of the punching cards mechanism presented in Fig. 1 is

composed from three beams OA=0.2 m, AB=0.5 m, DM=0.4 m and one triangle

BCD with BC=CD=0.35 m and BD=0.55 m. The length of OC distance is

OC=0.45 m. The punching cards mechanism is driven by a Rotary Motor applied

to the OA beam with constant rotational velocity n1=191 rot/min equivalent with

the angular velocity ω1=20 rad/s which corresponds to 1145.9 degree/second. The number of rotations during 1 sec is 3.18 and the time of one rotation is 0.314 sec.

The rigid angle α=150o between X direction and OC beam is constant. The start

ANALELE UNIVERSITĂŢII

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ANUL XXVI, NR.1, 2019, ISSN 1453 - 7397

182

position of the mechanism is defined by 210o angle between X direction and OA

beam. The analysis time of the study was imposed 1 sec. The point M move only

along Y direction and point C is fixed. The point O of the OA beam is connected to

Fixed part 1 and the point C of the CD beam is connected to Fixed part 2. This

study aims to compare the velocities and accelerations of A, B, D and M points,

calculated by grapho-analytical method and SolidWorks Motion module.

Figure 1. The punching cards geometry

3. Theoretical background and numerical results

The kinematic schema of the starting position mechanism was represented on

the k1=1/100 [ ] scale, Fig. 2 [3]. For the calculation of the velocities the kv =

ω1 k1 = 1/5 = 0.2 [ ] coefficient was used [3]. For the calculation of the

accelerations the kA = ω1 kv = 4 [ ] coefficient was used [3]. The velocities

and accelerations are calculated only for the start position of the mechanism by

grapho-analytical method through equations (1) ÷ (8) [3].

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Figure 2. The kinematic schema of the starting position mechanism

VA= ω1∙LOA; VA=20∙0.20 = 4 m/s (1)

�� � �� ∙ ��� �1

5 ∙ 18 � 3.6�/� (2)

�� � �� ∙ ����1

5 ∙ 18 � 3.6�/� (3)

�� � �� ∙ ����1

5 ∙ 14 � 2.8�/� (4)

�� � ��� ∙ !� � 20

� ∙ 0,2 � 80�/�� (5)

�� � �$ ∙ �$� � 4 ∙ 15,2 � 60.8�/�� (6)

�� � �$ ∙ �$�� � 4 ∙ 15,5 � 62�/�� (7)

�� � �$ ∙ �$��; �� � 4 ∙ 26 � 104�/�� (8)

184

4. The stages of Motion Study

The stages of the study are as follows [4] and [5]:

o Activation of the SolidWorks Motion module; o Creation and specification of the study’s options; o Specify Rotary Motor; o Specify Motion Mates; o Running the design study.

To specify Rotary Motor click Motor to create a new rotary motor; select the

face of the OA beam select Constant speed from Motor Type list and set 191 rpm

value in the speed motor field; click � and the Rotary Motor1 branch will be

created in the MotionManager design tree (Figure 4).

The mates indicated in Table 1 will be applied in Motion Study between the

assembly components. The mate Mate7 was only necessary to specify the

initial position of the mechanism, but before the motion analysis calculation

this mate must be suppresses.

Table 1. The mates applied to the punching cards mechanism

Mate

name

Mate

type

Component 1 Component 2

Mate1 Coincident Point O - Fixed part 1 Point O - beam OA

Mate2 Coincident Point A - beam OA Point A - beam AB

Mate3 Coincident Point C - Fixed part 2 Point C - beam CD

Mate4 Coincident Point B - beam AB Point B - beam DB

Mate5 Coincident Point D - beam DM Point D - beam CD

Mate6 Coincident Point M - beam DM Y direction

Mate7 Angle=210o X direction OA beam

5. Simulation and theoretical results comparison

For grapho-analytical method the velocities and accelerations were

calculated only for the start position of the mechanism, while in SolidWorks

Motion the results are calculated for the whole time of the study. The results

are presented as charts in Fig. 3 ÷ Fig. 10 and numeric in Table 2 and 3.

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Figure 3. The velocity of point A

Figure 4. The velocity of point B

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

0.0 0.2 0.4 0.6 0.8 1.0

Velocity point A

[m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.2 0.4 0.6 0.8 1.0

Velocity point B

[m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

186

Figure 5. The velocity of point D

Figure 6. The velocity of point M

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.2 0.4 0.6 0.8 1.0

Velocity point D

[m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.0 0.2 0.4 0.6 0.8 1.0

Velocity point M

[m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

187

Figure 7. The acceleration of point A

Figure 8. The acceleration of point B

60

65

70

75

80

85

90

95

0.0 0.2 0.4 0.6 0.8 1.0

Acceleration

point A [m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

0

50

100

150

200

250

0.0 0.2 0.4 0.6 0.8 1.0

Acceleration

point B [m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

188

Figure 9. The acceleration of point D

Figure 10. The acceleration of point M

0

50

100

150

200

250

300

0.0 0.2 0.4 0.6 0.8 1.0

Acceleration

point D [m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

0

50

100

150

200

250

300

350

400

450

0.0 0.2 0.4 0.6 0.8 1.0

Acceleration

point M [m/sec]

Time [sec]

SolidWorks Motion

Grapho-analytical

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Table 2. Numerical results from SolidWorks Motion

Time VA VB VD VM aA aB aD aM

sec m/s m/s m/s m/s m/s2 m/s2 m/s2 m/s2

0.00 4.00 3.45 3.45 2.74 80.01 60.83 60.83 95.36

0.04 4.00 4.11 3.45 5.60 79.30 60.83 60.83 27.50

0.08 4.00 3.21 3.45 4.37 80.06 60.83 60.83 78.85

0.12 4.00 1.41 3.45 1.35 79.99 60.83 60.83 57.47

0.16 4.00 0.53 3.45 0.46 80.10 60.83 60.83 44.23

0.20 4.00 3.03 3.45 3.63 80.18 60.83 60.83 143.27

0.24 4.00 7.31 3.45 9.80 79.95 60.83 60.83 39.21

0.28 4.00 0.83 3.45 0.41 72.16 60.83 60.83 97.07

0.32 4.00 3.71 3.45 3.29 80.02 60.83 60.83 93.67

0.36 4.00 4.05 3.45 5.72 80.03 60.83 60.83 10.09

0.40 4.00 2.99 3.45 3.90 79.78 60.83 60.83 80.02

0.44 4.00 1.13 3.45 1.03 80.10 60.83 60.83 52.26

0.48 4.00 0.82 3.45 0.73 80.03 60.83 60.83 48.96

0.52 4.00 3.56 3.45 4.55 80.22 60.83 60.83 171.32

0.56 4.00 7.52 3.45 9.15 80.29 60.83 60.83 180.23

0.60 4.00 0.41 3.45 0.20 77.82 60.83 60.83 88.71

0.64 4.00 3.89 3.45 3.83 80.01 60.83 60.83 88.73

0.68 4.00 3.97 3.45 5.72 80.00 60.83 60.83 8.37

0.72 4.00 2.74 3.45 3.40 79.98 60.83 60.83 83.10

0.76 4.00 0.84 3.45 0.75 79.99 60.83 60.83 47.09

0.80 4.00 1.13 3.45 1.04 80.03 60.83 60.83 56.32

0.84 4.00 4.15 3.45 5.61 80.20 60.83 60.83 194.01

0.88 4.00 7.28 3.45 7.70 91.17 60.83 60.83 381.19

0.92 4.00 1.40 3.45 0.71 79.86 60.83 60.83 84.53

0.96 4.00 4.01 3.45 4.33 80.01 60.83 60.83 80.89

1.00 4.00 3.86 3.45 5.62 80.01 60.83 60.83 26.67

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Table 3. Numerical results comparison

Parameter Time VA VB VD VM aA aB aD aM

Units sec m/s2 m/s

2

Grapho-

analytical 0.00 4.00 3.6 3.6 2.8 80 60.8 62 104

SW Motion 0.00 4.00 3.45 3.45 2.74 80.01 60.83 60.83 95.36

4. Conclusion

We have presented the required steps to analyze the punching cards

mechanism and obtain the kinematic parameters through grapho-analytical method

and SolidWorks Motion software. The numerical values calculated by grapho-

analytical method were compared in Table 3 with the SolidWorks Motion results.

The magnitudes of all results indicated a very good agreement with the values

obtained by analysis in SolidWorks Motion software.

References

[1] Cortada J.W., Before the Computer, IBM, NCR, Burroughs, & Remington

Rand & The Industry They Created, Princeton University Press, 2000. [2] Lubar S., Do Not Fold, Spindle or Mutilate. A Cultural History of the Punch

Card, Journal of American Culture, 1992, pp. 43- 55.

[3] Anghel St., Ianici S., Mecanisme plane articulate. Probleme applicative,

Editura Eftimie Murgu, Resita, 2001.

[4] Dassault Systems 2010 SolidWorks Motion, 300 Baker Avenue, Concord,

Massachusetts, 01742, 2010, USA.

[5] Nedelcu D., Nedeloni M.D., Daia D., The Kinematic and Dynamic Analysis of

the Crank Mechanism with SolidWorks Motion, Proceedings of the 11th

WSEAS International Conference on Signal Processing, Computational

Geometry and Artificial Vision, Italy, 23-25 August 2011, pp. 245-250.

Addresses:

• Prof. Dr. Eng. Dorian Nedelcu, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, d.nedelcu@uem.ro

• Prof. Dr. Eng. Gilbert-Rainer Gillich, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, gr.gillich@uem.ro

• Prof. dr. Istvan Biro, Faculty of Engineering, University of Szeged, Mars tér 7, H-6724 Szeged, biro-i@mk.u-szeged.hu

• Lect. Dr. Eng. Habil. Zoltan-Iosif Korka, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, z.korka@uem.ro

• PhD student Attila Gerocs, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, a.gerocs@uem.ro